Note that our choice of binning is chosen by eye, simply requiring that the reconstructed signal visually matches the fiducial one. The more sophisticated SGWBinner approach of Ref. [1]} iteratively selects the width and number of each bin by using statistical arguments based on information criteria. The results of this Section clearly show the need to apply such advanced reconstruction tools, opening to the possibility to test PBHs and the thermal history of the Universe through the reconstruction of the SGWB.
